Unlike physical observables, individual scattering amplitudes in QFT generally possess
infraredWe use the term “infrared” (IR) to denote both soft and collinear divergences.
(IR) and ultraviolet (UV) divergences, and thus a regularization scheme (RS) for handling these
intermediate divergences needs to be introduced.
Dimensional regularization [1]}, [2]} is by far the most convenient one
to use in gauge theories as it respects gauge and Lorentz invarianceWe ignore the treatment of
\(\gamma _5\)  in dimensional regularization for the moment.
and allows one to handle both UV and IR divergences in the same manner.
The key ingredient of dimensional regularization is the analytic continuation of
loop momenta to \(D=4-2\epsilon \)  space-time dimensions with indefinite \(\epsilon \) .
Having done this, one is still left with some freedom regarding the dimensionality of the momenta
of the external particles, of algebraic objects like the space-time metric tensor and Dirac matrices,
as well as the number of polarizations of both external and internal particles.
This gives rise to different dimensional regularization variants (for a review see e.g.
ref. [3]} and references therein), which in general leads to different
expressions for singular amplitudes.
Apparently the RS dependence is intimately connected to the singularity structures of amplitudes,
which fortunately obey a nice factorization form at the amplitude level [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}.
The result for a physical quantity, such as a physical cross section which is free of any such divergence,
must not depend on the RS that has been used.
However, in practice, such a result is obtained as a sum of several partial contributions,
which usually are individually divergent and computed separately before being combined.
Therefore, these intermediate results can depend on the RS, and have to be computed consistently
to ensure the cancellation of the spurious RS-dependence.
